SOLUTION: Please help me find {{{ a }}}, {{{ b }}} & {{{ c }}} for the function {{{f(x)}}}{{{""=""}}}{{{a*sin(bx+c)}}}. The graph of {{{ f }}} must match this graph below. Graph: htt

That's a sine graph shifted left from the origin (0,0)
to the first x-intercept left of the x-axis.



Since the highest it goes in 2, and the lowest it goes is
-2, the amplitude, a, is 2.
So we have so far:



The period is given by the formula 

Each mark on the x-axis represents π because there
are 6 of them and the 6π at the right end of the graph
lets us know that each mark counts as π.

We can tell the period because it's the distance along
the x-axis from 1 peak to the next.

The peak marked (-π/2,2) has x-coordinate -π/2 and the
next peak is halfway between 3π and 4π which is , 
or  or . So the period is the 
difference of these two x-values, which is 


Since the period is given by the formula , we have
the equation:  



Multiply both sides by b



Divide both sides by 4π



Cancel the π's:





So we have so far:



Finally we need to know the phase shift which is ,
right if it's negative and left if it's positive.

The first x-intercept left of the origin is halfway
between -π and -2π which is , 
or  or . 

So c = that with a positive sign since it shifts left from (0,0,)



So the final answer is



Edwin